Legal Name Change After Marriage

If a spouse in India changes its name after marriage, the husband keeps the name as his surname and also adopts the surname of her husband, she changed her identity completely OldFirst OldMiddle OldLast to NewFirst Husband's_First Husband's_Last. We only have a marriage certificate that lists both the old and new names for this topic. While the processing of green cards in the U.S., USCIS is asking for more evidence on this legal name change. Can anyone please suggest what other legal documentation can we providea

SSA, the Social Security Administration, you will receive your SSN in your new name. Complete forms using your SSN USCIS again with your new name.